ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 10 Mar 2017 14:25:21 +0100How to get the quotients in multivariable polynomial division?https://ask.sagemath.org/question/36901/how-to-get-the-quotients-in-multivariable-polynomial-division/Given a Groebner basis $G=\lbrace f_1,\dots,f_s \rbrace$ and $g$, how can I get the quotients of $g$ on division by $G$ ? I know that when considering the quotients, the ordering we use to list the divisors $f_1,\dots,f_s$ matters. I also know the command `p.reduce(I)` for remainders. I would appreciate any help with this situation.Fri, 10 Mar 2017 13:47:41 +0100https://ask.sagemath.org/question/36901/how-to-get-the-quotients-in-multivariable-polynomial-division/Comment by tmonteil for <p>Given a Groebner basis $G=\lbrace f_1,\dots,f_s \rbrace$ and $g$, how can I get the quotients of $g$ on division by $G$ ? I know that when considering the quotients, the ordering we use to list the divisors $f_1,\dots,f_s$ matters. I also know the command <code>p.reduce(I)</code> for remainders. I would appreciate any help with this situation.</p>
https://ask.sagemath.org/question/36901/how-to-get-the-quotients-in-multivariable-polynomial-division/?comment=36905#post-id-36905Could you please provide the construction of the `fi` and `g` so that we start from something concrete, without having to build our own ?Fri, 10 Mar 2017 14:25:21 +0100https://ask.sagemath.org/question/36901/how-to-get-the-quotients-in-multivariable-polynomial-division/?comment=36905#post-id-36905